This paper develops a model to analyze asymmetric competition between multi-product retail channels, highlighting a novel interaction between vertical double marginalization and horizontal multiple marginalization. The interplay between these forms of marginalization creates two distinct types of pricing incentives for each upstream party in a retail channel. Both within-channel and cross-channel incentives drive upstream prices upward, but their effects on retail competition and prices vary significantly, depending on whether retail channels are operating in reseller or marketplace models. We consider the heterogeneity of retailer buyer power across different producers and examine the implications of increasing retailer buyer power and shifting business models on retail prices, retailer and producer profits, and consumer welfare.